The logic of Bunched Implications, through its intuitionistic version (BI) as well as one of its classical versions called Boolean BI (BBI), serves as a logical basis to spatial or separation logic frameworks. In BI, the logical implication is interpreted intuitionistically whereas it is generally interpreted classically in spatial or separation logics like in BBI. In this paper, we aim at givi...

In this research note, we introduce a graded BDI agent development framework, g-BDI for short, that allows to build agents as multi-context systems that reason about three fundamental and graded mental attitudes (i.e. beliefs, desires and intentions). We propose a sound and complete logical framework for them and some logical extensions to accommodate slightly different views on desires.

It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with impredicative polymorphism and recursive types. We show that the resulting logical relation is sound and complete with respect to the contextual preorder and...

We present a proof technique, based on syntactic logical relations, for showing contextual equivalence of expressions in a λ-calculus with recursive types and impredicative universal and existential types. We show that for recursive and polymorphic types, the method is both sound and complete with respect to contextual equivalence, while for existential types, it is sound but incomplete. Our de...

This paper presents a novel syntactic logical relation for System F◦, a simple variant of the linear polymorphic λcalculus. We define a logical relation for open values under both open linear and unrestricted contexts, then extend it for open terms with evaluation and open relation substitutions. Relations that instantiate type quantifiers are for open terms and types. We demonstrate the applic...

Most rule-based systems are imperative, or, if they are mainly declarative, also provide some imperative features. It is argued that a strictly declarative formalism with a sound logical basis is